Let D be any integral domain of any characteristic. A polynomial p(x) ∈ D[x] is D-nice if p(x) and its derivative p′(x) split in D[x]. We give a complete description of all D-nice symmetric polynomials with four roots over integral domains D of any characteristic not equal to 2 by giving an explicit formula for constructing these polynomials and by counting equivalence classes of such D-nice polynomials. To illustrate our results, we give several examples we have found using our formula. We conclude by stating the open problem of finding all D-nice symmetric polynomials with four roots over integral domains D of characteristic 2 and all D-nice polynomials with four roots over all integral domains D of any characteristic.
Critical point D-nice polynomial integral domain nice polynomial polynomial root symmetric polynomial
Diğer ID | JA72SA48AB |
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Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 1 Aralık 2007 |
Yayımlandığı Sayı | Yıl 2007 Cilt: 2 Sayı: 2 |